Unlike video files that usually only support a constant frame rate, there’s an individual delay between frames in the animated image file formats like AGIF, APNG¹, MNG or SVG+SMIL². This (and often the lack of sound) is a fundamental difference which simple video to GIF converters cannot take advantage of. I don’t know whether there are advanced ones that can automatically determine such values.
The default, minimum, maximum, median and average, hence optimal frame rates, accordingly, depend a lot on the nature of the video or animation. Think of a cheap 1980s Japanese anime, large portions of which would be fine with 1 Hz. Usually you should be good with 12–15 Hz, although you probably know that higher (progressive) rates of 24, 25 and 30 Hz (or double that) are used in cinema and television.
Be also aware that some browsers may actually slow down GIFs with too high a frame rate, which can start at 20 Hz.
The Graphics Interchange Format is not intended as a platform for
animation, even though it can be done in a limited way.
— GIF89a – Appendix D “Conventions”